Here are some questions that relate to expectations about circles within circles, and spatial perception more generally.
• Suppose we take a large circle and put six small circles inside it. Do you expect any special features to restrict the way the small circles can be arranged? If we impose some constraints on the configuration — for example, each small circle must touch the large circle and its two small circle neighbours — do you expect any special features will then come into play?
• Imagine such a configuration in which there are 10 identical small circles. How big do you predict the large circle must be to accommodate the configuration?
• If the large circle is three times the radius of a set of identical small circles, how many small circles do you predict can be placed, without overlap, inside the large circle? What if the large circle is four time the radius of the small circles?
I was prompted to think about some questions like this after I made a post about overlapping circles in a welcome note to a new Stampboards member: